Algorithmic Differentiation, Applications in Monte Carlo

Specialeforsvar ved Frederik Johannes Kryger-Baggesen

Titel: Algorithmic Differentiation; Applications in Monte Carlo

Abstract: In the field of mathematical finance, Monte Carlo simulation has proven to be a useful technique to valuate derivatives. While being easy to understand and implement, its disadvantage lies in computational efficiency. Especially in the computations of risk sensitivities, Monte Carlo simulation can be very inefficient. This thesis explores the computational benefits of applying algorithmic differentiation within Monte Carlo simulation. By implementing algorithmic differentiation in way that requires minimal programming, this thesis still finds that the computations of risk sensitivities can be accelerated by great magnitudes. It exploits the efficient risk sensitivities in the task of model calibration, and finally demonstrates how to take advantage of this, to convert the risk sensitivities into market risk by an application of the Implicit Function Theorem. Keywords: Algorithmic Differentiation; Monte Carlo simulation; Implicit Function Theorem, Model Calibration.

Vejleder: Rolf Poulsen
Censor:   Elisa Nicolato, Aarhus Universitet